which amounts to the assumption of \(S\)  independent invariance constraints on the \(S\)  distinct sensitive attributes.Note that this does not necessarily imply “subgroup fairness” on the joint distribution [1]}.
Importantly, we assume that the set \(S\)  is not fixed (e.g., different users might request different invariance constraints).
In the language of algorithmic fairness, the representational invariance of Equation (REF ) implies that traditional demographic parity constraints are satisfied on the sensitive attributes and recommendations.
